Consider two firms who compete in Bertrand, with MC = 2 and demand equal to =202
ID: 1114910 • Letter: C
Question
Consider two firms who compete in Bertrand, with MC = 2 and demand equal to =202Q.
(a) Suppose the firms decide to collude for a finite number of periods. Would collusion be sustainable? Why?
(b) Suppose that the firms decide to collude for an infinite number of periods, explain under what conditions over the discount factor is collusion sustainable.
(c) Suppose that firms realize that it is to costly to punish forever the opponent after a deviation and decide on a strategy in which the punishment takes place for 2 periods, and then they revert to cooperation. Would collusion be sustainable in this case? Under what conditions over the discount factor?
Explanation / Answer
A) No firm will not be able to collude bacause of backward induction and both will play nash equilibrium
B) when firm decide to collude for infinite period then
Payoff from collusion=monopoly profit/2(1-d)
If one deviate then expected payoff=monopoly profit
Collusion is sustainable when 1/2(1-d)>1
1>2-2d
d>1/2
C)expected payoff from devaitaion=monopoly profit
Monopoly profit/2*(1+d+d2)=monopoly profit
(1+d+d2)=2
d2+d-1=0